Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
Correct Answer
$7192
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5800 × 3% × 8
= $5800 ×3/100 × 8
= 5800 × 3 × 8/100
= 17400 × 8/100
= 139200/100
= $1392
Thus, Simple Interest = $1392
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $1392
= $7192
Thus, Amount to be paid = $7192 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5800
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 3% × 8)
= $5800 + ($5800 ×3/100 × 8)
= $5800 + (5800 × 3 × 8/100)
= $5800 + (17400 × 8/100)
= $5800 + (139200/100)
= $5800 + $1392 = $7192
Thus, Amount (A) to be paid = $7192 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5800, the simple interest in 1 year
= 3/100 × 5800
= 3 × 5800/100
= 17400/100 = $174
Thus, simple interest for 1 year = $174
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $174 × 8 = $1392
Thus, Simple Interest (SI) = $1392
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $1392
= $7192
Thus, Amount to be paid = $7192 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.
(4) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(7) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?